Exponent Guy

An antique coin appreciates in value the older it gets. The following data shows that the value of a certain coin for every year since it was purchased.

x

# of years since purchased

0 1 2 3 4 5 6 7 8 9

y

Value of coin in $

3 3.45 3.98 4.58

a) Using a graphing calculator with Diagnostics turned on, determine the function for this relationship.

xy )15.1(3

a initial value, when x = 0 b common ratio (app by 15%)

xy )15.1(3

How long does it take for the coin to double in value? x)15.1(36

3

)15.1(3

3

6 x

x)15.1(2 5x

xy )15.1(3

Now if we take into consideration these two points (0 , 3) and (5, 6) as two points on the curve and replace the doubling effect as 2 for the base, how else can we represent this scenario?

5)2(3x

y 3 is the initial value when x = 0

2 is the base to show the price is doubling.

5 is the time it will take to double.

Try Page 136 # 30

x 0 2 4 6

y 200 18 1.62 .1458

Determining a Function from a Table

09.0200

18b

200a

2c

c

x

bay )(

2)09(.200x

y

More Examples:1. An investment triples every six years. If you invest $2500, how

much will it be worth after 25 years?

6)3(2500x

y 6

25

)3(2500y73.189,243$y

After 25 years, the $2500 investment would be worth $243, 189.73

2. A house appreciates by 10% every 4 years. How much would a $100,000 house be worth in 20 years?

4)1.1(000,100x

y 4

20

)1.1(000,100y051,161$y

After 20 years, the house could sell for $161, 051.

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The More Practice, the Better! Page 150

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